Everything owes a debt to nothing

How can you write a book about nothing? Or, in this instance, two books. The answer is by broadening the meaning of nothing from the invention of the zero in arithmetic to the vacuum of outer space. Both John Barrow, a theoretical physicist, and Charles Seife, a science journalist, have done just this, and have written informative and entertaining books in the process. Both begin with the invention of zero as a placeholder by the Sumerians and end with the big bang and the creation of the universe. But although the two books cover much common ground between these similar start and end points, Barrow and Seife take sufficiently different routes that reading them both is worthwhile.

Barrow's book exudes erudition from the start. Even in chapter nought, there are references to J. K. Galbraith and Ali G, to artists Ad Reinhardt, Robert Rauschenberg and Jasper Johns, to musician John Cage's composition 4 ' 33 " - a composition of total silence - and to Gogol's Dead Souls . His account of the origin of zero is well researched. It takes the reader from the Sumerian, Babylonian and Mayan invention of zero as a placeholder in a positional system of numbers, to the Hindu invention of zero in our modern algebraic sense where zero is not only a placeholder but also the result of taking 5 from 5. Barrow contrasts the Indian tradition - in which the word for zero represented a wealth of concepts from the numerical zero to the void from which the world was created - with that of the Greek tradition typified by Parmenides, who argued that empty space could not exist, and by the Pythagoreans, who thought of numbers in terms of shapes.

A novel feature of Barrow's book is his examination of the literary use of nothing. As early as the 5th century AD, St Augustine's identification of nothing with the devil - representing complete separation from God - and the subsequent religious debates meant that writers and philosophers invented paradoxes and puns as a way of playing with the demonic concept of empty space in a politically acceptable way. Zero, being shaped like an egg, also became a symbol of new life, and in Elizabethan times, zero as a circle was also an allusion to female sexual genitalia. Barrow gives some fascinating examples from Shakespeare's plays - The Winter's Tale , Much Ado about Nothing , Hamlet , Macbeth and King Lear . He also quotes a wonderfully meaningless ramble by Sartre on negation and nothingness.

The feature I liked best in Seife's book was his inclusion of the role of zero as an infinitesimal quantity in the invention of calculus. The famous dispute between Newton and Leibnitz is here, along with a reference to one of Kepler's lesser-known works on the "Volume measurement of barrels". Despite the manifest evidence that differentiation and integration using this new calculus clearly worked, there was much suspicion about the legitimacy of manipulating quantities that were infinitesimally close to zero. Bishop Berkeley went so far as to refer to infinitesimals as "ghosts of departed quantities". Seife outlines how the concept of the limit made these zeros respectable and then goes on to survey the discovery of the complex plane and the mapping of zero and infinity to the Reimann sphere. In this way, Seife's book becomes as much about infinity as about zero.

Apart from these diversions, the two books cover much the same ground. Seife's discussion of Greek mathematics appealed to me more because it gave the right amount of historical background and concentrated on essentials. In Barrow's book, I learnt about Parmenides, Zeno (of the paradox), Aristotle, Empedocles, Anaxagoras, Leucippus, Democritus, Epicurus, Pythagoras, Zeno of Cition ("not to be confused with Zeno of the paradoxes"), Chrysippus and Poseidonius. Although interested in the history of the evolution of scientific ideas, there is a limit to how much I want to know about primitive ideas of the past and who did or thought what. Here, the scholarship is so much on display that it distracts from the basic story.

When the books get on to physics, however, Barrow has the edge. Although Seife tells a good story with a great deal of style, he makes a number of questionable assertions. About the discovery of absolute zero, Seife says this "was the beginning of a new branch of physics: thermodynamics". In fact, thermodynamics began with Carnot and the study of steam engines in the early 19th century. There is a similar throwaway inaccuracy in his account of the Nobel prizewinning discovery of cosmic microwave background radiation by Arno Penzias and Robert Wilson at Bell Labs. Seife comments that "many scientists" think it unfair that theorists Bob Dicke and Jim Peebles at nearby Princeton University who helped Penzias and Wilson understand what they were seeing, were not rewarded by the Nobel prize committee. In fact, as George Gamow had written about the microwave background radiation as a relic of the big bang in a popular science book some years before, this remark seems out of touch. There are not many such examples, but sufficient to give me some doubts. Was Kepler ever a monk? I also find Seife's hyperbolic style rather irritating. Of the discovery of perspective and vanishing points by painters, he says: "Zero had transformed the art world." After a discussion of black holes: "Zero is so powerful because it unhinges the laws of physics." About the heat death of the universe: "The answer is ice, not fire, thanks to the power of zero." And many more.

But these are minor blemishes: both books are well written, readable and contain much that is interesting. Both discuss Torricelli's wonderfully simple experiment that demonstrated the creation of a vacuum. Both include good accounts of Casimir's mysterious vacuum force and give credit to Steve Lamoreaux for measuring it directly. Both survey the origins of quantum mechanics and relativity. Einstein's demolition of the all-pervasive aether and his introduction of the cosmological constant are covered, along with modern theories about string theory and the inflationary universe. A puzzling omission from both books is any serious discussion of the electroweak vacuum. This is the accepted theory of weak and electromagnetic forces and requires us to believe that we are living inside something like a weak-force version of a superconductor! It seems to me that this would have been a better exemplar than more speculative and remote theories of the early universe.

My final criticism is aimed not so much at these authors but at popular science publishers in general. The popularisation of science is now an established business for publishers and booksellers. The traditional formula for a "trade" book on popular science is a text of about 200 or so pages with black-and-white diagrams and pictures. The target audience is the educated reader with a general interest in science. At the other end of the scale, we have well-illustrated science reference books such as encyclopedias or atlases. These two books fit the first of these categories. My problem with this state of affairs is that such books are rarely very accessible or attractive to young people still at school. With the treadmill of the national curriculum, a popular science book needs to be very well targeted to excite their enthusiasm and capture their imagination. This is not to say that such books should attempt to make "easy" what is essentially an intellectually demanding but ultimately rewarding journey. To understand the Maxwell or Schrodinger equation requires an understanding of differential calculus, curvilinear coordinates and so on. We should not minimise the difficulty but emphasise the wealth of understanding of the universe that such mastery opens up. Given the increasing technological fragility of our society, exciting young people about science as well as entertaining general readers should be the ambition of science publishers and government.

Tony Hey is professor of computation, University of Southampton, and author of two popular science books.